Yes. But I warn you the plugin will not help you with that image. The plugin is intended to run images in daemon mode. That handbrake image is for running in interactive mode, cli terminal.

docker run -it -v /video/folder:/videos imagename bash

Will put you inside the container, you can go to /videos folder and run handbrake cli command to convert files, make sure the output is to the same video folder so you can gather the file from the host side

Just drop down to terminal to run the containers. You're already looking for handbrake-cli, not handbrake-gtk.
I haven't looked at handbrake images lately, But I am pretty sure they are all the same. In the docker hub you can search and look for the most popular, that's what I usually do.

This is gonna continue endless if you don't start reading about how docker/containers really works.
Docker does not see host path because is a container, is isolated. If you want data to be accessible from the container you use a mount bind with the -v switch -v /media/uuid/videos:/videos

Now that's part of the docker command argument not handbrake argument

Now the long path is accessible in the container from /videos

So in your command you'll have to change the path to -i /videos/TSFOLDER for example